# Talk:Cournot competition

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## Untitled

Ceteris Paribus is didactic and archaic language, let's not use it QUITE so much, fellow economists.

—Preceding unsigned comment added by Aaronchall (talkcontribs) 19:23, 10 February 2009 (UTC)

The formula for N firm equilibrium quantity doesn't match my textbook or lecture notes - should it be as follows?

$\ q_i = q = \frac{a-c} {(N+1)b}$

(note extra b on the bottom of the fraction)

You are correct sir. Using the equation as given on the page currently will give the reader incorrect quantity. —Preceding unsigned comment added by 66.230.88.149 (talk) 06:43, 1 April 2010 (UTC)

Formula for q sub i has been corrected as discussed. I'll derive the equation from scratch later so readers can follow the logic for themselves —Preceding unsigned comment added by 66.230.88.149 (talk) 11:38, 2 April 2010 (UTC)

Formula for N firm total quantity should be:

$Nq = \frac{N(a-c)} {(N+1)b}$

(note extra N on the top of the fraction)

EdEgan (talk) 01:24, 24 March 2013 (UTC)Hi Guys. There was an error in the math in the Cournot competition with many firms and the Cournot Theorem subsection in the calculation of the N and q with endogenous entry. The previous math assumed b=1 to give:

$N=(a-c)/ \sqrt{F}-1$
$q=\sqrt{F}$

I posted the corrected math for the general case:

$N=\frac{(a-c)}{\sqrt{Fb}}-1$
$q=\frac{\sqrt{Fb}}{b}$

--78.104.152.228 (talk) 14:58, 12 April 2010 (UTC)

What is N? The first mention of the variable doesn't define it.

I second this. Can somebody please define N? I believe it supposed to be the number of firms in the market, but I can't confirm as I am a lowly undergraduate.

Yes, N is the number of firms in an industry.

The text explanation of the diagrams needs to be made a bit clearer. I have made some minor edits but don't have the expertise to rewrite them

## Homogeneous?

It seems to me that the goods should be non-homogeneous (but still competing, obviously) since the strategy for one firm is to monopolize its share of the market. With homogeneous goods, buyers would flock to the cheaper version. I like to think of it in terms of Macintoshes vs. PCs-- they're non-homogeneous, but both sides are monopolizing their market share. If I'm wrong, why should homogeneous products be central to Cournot competition?--134.173.58.54 04:16, 10 December 2006 (UTC)

What you're referring to would be a variant of Bertrand competition. In Cournot competition firms don't set price, the market does. The firms just deliver the goods to the market. Hence, it's competition in quantity, not price, which is the distinguishing feature of Cournot model. As a result there's always only a single price and it makes sense for goods to be homogenous. There are some Bertrand-Cournot hybrid models where the firms still compete in quantities but goods are differentiatied - however, these are roughly equivalent to the simple Cournot model with a homogenous good but different cost structures (let me stress the "roughly" in that sentence).radek 19:21, 10 December 2006 (UTC)

What is "a"? —Preceding unsigned comment added by 81.110.27.62 (talk) 16:48, 17 February 2008 (UTC)

The intercept of the demand curve.radek (talk) 04:19, 18 February 2009 (UTC)

Originally, in Stackelberg versus Cournot section, there is a sentence as follows.

• Above is an example of too much information hurting a player.

Then I changed it as follows.

Many people refer to the above as "an example of too much information hurting oneself". However, this is not true. Actually, the follower is still hurt by the lack of information, while the leader takes advantage of knowing more information (explanation as follows).

In fact, the leader can take the stackelberg position because the leader knows that the follower knows the leader's chosen quantity and that the followers thinks the leader doesn't know the follower's chosen quantity (and that the follower is rational)(three conditions, the last one is trivial). On the other side, the follower doesn't know whether the leader knows the follower's chosen quantity, if the follower knows that the leader knows the follower's chosen quantity, then it is safe for the "follower" to choose the cournot position if the "follower" is still not sure whether (doesn't knows that) the "leader" thinks the "follower" doesn't know the "leader"'s chosen quantity, and it is safe for the "follower" to choose the Stackelberg position if the "follower" is sure (knows) that the "leader" thinks the "follower" doesn't know the "leader"'s chosen quantity. The meaning of this scenario explains the common phenomenon that people tends to tell other people what they will do, and doesn't want to hear what the opponent will do. (People doesn't want to hear doesn't mean they doesn't want to know, but they doesn't want the opponent knows they know.)

However, my editing was deleted by Radeksz who left a note and did not discuss with me as I hoped. (I deem Radeksz as arrogant although he/she has the right to do so.): I'm sorry but this is wrong - there's common knowledge of rationality on both sides. My response to this:

In the cournot competition, yes, symmetric, but in the stackelberg competition, the game is not symmetric, and the leader acts first. What I wrote elaborates the difference between them, and it is right. What I wrote explains when the competition game is cournot, and when the game is stackelberg. Though, it might be more appropriate to be put under the Stackelberg_competition#Stackelberg_compared_with_Cournot section.

Jackzhp (talk) 02:34, 21 February 2009 (UTC)

Jackzhp, didn't mean to come off as arrogant. But your description was incorrect. Both players in a Stackelberg game have the same (perfect) information, just like in the Cournot game. In particular the statement "the followers thinks the leader doesn't know the follower's chosen quantity" is wrong. The followers knows that the leader knows what the follower's chosen quantity will be. And in turn the leader knows that the follower knows that the leader knows what the follower's chosen quantity will be. And so on ad infinitum (this is the definition of "Common Knowledge of Rationality"). In fact they both know exactly what the outcome will be before the game is even played - that's the nature of an equilibrium. The advantage to the leader comes not from differences in information or knowledge but rather from the ability to commit to a particular quantity level before the follower makes her choice.
While we're on the subject, perhaps it should be clarified in the article (or in the Stackelberg one) that in the Stackelberg-type game with price (Bertrand) competition and differentiated goods it's the follower that has the advantage. Basically if the choices are strategic complements, as they are in Stackelberg-Bertrand, (reaction functions slope up) there's a second mover advantage while if the choices are strategic substitutes, as in Stackelber-Cournot, (reaction functions slope down), there's a first mover advantage. I'm doing this from memory so it should be double checked (don't want to come off as arrogant). But none of this has anything to do with information but rather with whether commitment hurts or benefits you.radek (talk) 03:17, 21 February 2009 (UTC)
This: "There is also the important assumption of perfect information in the Stackelberg game: the follower must observe the quantity chosen by the leader, otherwise the game reduces to Cournot." is also not technically correct.
Basically, if you're gonna say something like that you have to be specific about what you mean by 'imperfect information'. In particular you have to say 1) what the follower actually observes and reacts to and 2) how the leader forms her beliefs about what the follower knows. Suppose both firms are risk neutral, the follower doesn't know c(q1), and that the follower observes the leader's output imperfectly in the sense that she observes q1*=q1+e where q1 is the actual q chosen by the leader and e is a random white noise term (this generalizes to basically any model with E(e)=0). Then the follower will choose q2 as best response to q1+e. The leader knows how the follower forms their observation but she doesn't know what e will be. But since E(e)=0 the best she can do is to act as if the follower was going to choose q2 as best response to the actual q chosen by the leader, q1. As a result, introducing imperfect information here in no way changes the equilibrium (though there will be random variation around it in terms of q2). So it's not true that the game reduces to Cournot.
Additionally, it's actually not necessary that the follower observe q1. An assumption that she knows c(q1) (and of course p(q1+q2)) is sufficient. There might be some other belief formation/imperfect info models where Stackelberg reduces to Cournot (find some sources folks) but the above is not true generally. The Stackelberg article has more problems than this one though.radek (talk) 03:41, 21 February 2009 (UTC)

At first, thank you for the discussion! I appreciate it. Your response gave me an idea the way how you reasoned through the problem, and, by reading your response, I know that it will be very difficult for me to convince you. I will leave three points in good faith. 1. The quotation you mentioned was not written by me, and I also deem it incorrect, but for different reason which I have written above (and which is the subtitle of this discussion). 2. In fact, it is not the simultaneity of the game makes the Stackelberg from Cournot, but the information set based on which the leader & the follower makes decision. In the literature, for convenience, people use simultaneity to imply the same information for Cournot, and different information set for Stackelberg. And, it is the information set defines the player as the leader or the follower. Let's restate my point one more time. The situation A {I know Z, you know Z}, situation B {I know Z, you know Z, I know you know Z, I know you don't know whether I know Z or not}, situation C {I know Z, you know Z, I know you know Z, you know I know Z, I know you know I know Z, you know I know you know Z}. A, B & C are very different, C is symmetric, the information specified in C is for both players in Cournot, B is analog to the Stackelberg, information set specified in B is not symmetric, and one is for the leader, another one is for the follower. By the way, in A, many things are unspecified.

The information set in B: {I know Z, I know you know Z, I know you know I know Z} -- the common knowledge & rationality. The information set in C: {I know Z, I know you know Z, I know you don't know whether I know Z} & {I know Z, I know you know I know Z, I don't know whether you know Z}.

If I make you feel dizzy, I am very sorry. Let's try my 3rd point. 3. Suppose we are playing the Stackelberg game, you are the leader (I let you move first), then you will choose the leader's quantity position, and let me know your quantity by whatever means, and you hope I will follow. However, I am a little bit "weird", instead, I choose the leader's quantity position, and make sure you know this, and I don't listen to you anymore, then you will be forced to choose the follower's quantity position because that will be your best response (assume you are rational).

If you are still not convinced, let's forget about the game, and let's go to get something to eat/drink instead. Cheers! Jackzhp (talk) 18:15, 21 February 2009 (UTC)

Jack, sorry, not convinced as you say. Both Stackelberg and Cournot are games of perfect information (they both know that each other knows that the other knows that the other knows...), roughly speaking, the situation C. If you could provide any links to the literature (preferably published papers or classic books on the topic like Fudenberg and Tirole) that characterizes the difference between Stackelberg and Cournot in terms of information sets I would be definietly interested in taking a look.radek (talk) 20:56, 21 February 2009 (UTC)

Maybe in a later day. best regards. Jackzhp (talk) 22:17, 21 February 2009 (UTC)

## Too technical for most readers to understand?

This page has been tagged as being too technical for most readers to understand since March of 2009, but it does not seem too technical to me. Unless someone objects, I am going to wait seven days and then remove the tag. Guy Macon (talk) 02:09, 10 March 2011 (UTC)

Removing tag now. Guy Macon (talk) 18:24, 19 March 2011 (UTC)